I get what you're saying, but it's always been sort of a variant wizard. I want WotC to keep looking for that sweet-spot where the psion can fill the same basic role as the wizard (same way a sorcerer or warlock or even bard does), but also does it in its own unique way (like those classes).
There's a few things at work here -- first, I don't know what "role" one needs filled there. Wizards can fill lots of roles. Any class can fill lots of roles. There's no need for a wizard, sorcerer, bard, or warlock (or any particular class) in any party. So there's nothing inherently special and necessary in a wizard. You play a wizard like you play a paladin or a fighter or a rogue -- because you WANT to.
The next is that I could imagine an independent psionic class, but they need the mechanical "size" to back that up. They needs something mechanically distinct that alters how they use their "spells," a la a warlock's at-will/encounter casting or a sorcerer's sorcery points. And it couldn't be either of those things. They can't just be the same features of a wizard (high-level spells, versatility in selection, tradition features, etc.) but "it's psionic so it's not the same!" That's hypothetically possible, I imagine, but I'm not sure what that would look like. A points system isn't enough to distinguish it by itself.
I don't hate the idea of a "wild talent" feat that allows exactly what you've described, but how can we balance a dedicated psionic character whose powers are all external to their primary class?
Feats could pick up much of that slack. Want to be a dedicated psionic character? Sounds good, you'll just be giving up higher ability scores in exchange for several psionic feats ("I've learned
ego whip,
pyrokinesis, and
Tower of Iron Will with this feat!").
I see. I think I'm with you 90%; I just don't think the wizard framework is ideal for psions--too much "book magic" built into the core of the class, even if the crunch-execution is similar to the ideal psion.
The only thing about a wizard that is "book magic" is the spellbook, whose only mechanical function is to allow the wizard to load out a different list of spells known each day. One variant feature might replace that (maybe a "psionic focus" ability that gives the School of Psionics wizard a small perk in exchange for not spending all of their spell slots or something).
Psionics has long stood as an alternative to magic. If all else fails to make psionics worthwhile, I think it's worth including just for the very different flavour of pikes and psychics compared to swords and sorcery. YMMV.
I guess I don't understand why a subclass or several wouldn't give that alternative flavor without all the labor-intensive fobs of a whole new class.
A few new wizard schools (Seers, Telepaths, Kineticists, Nomads, Egoists, Creatives) with some new features support the "dedicated mind-mage" archetype. Psychic warriors are just another fighter variant. Monks could become soulknives. Sorcerers would make good wilders ("I just have this power, I don't know what to do with it!") Heck, we could even dust off the Lurk for rogues and the Ardent for bards and the Divine Mind for Paladins (though I'm not sure any of those are missed very much). There's not much in the existing suite of psionics that doesn't fit snugly into subclass territory.
IMXP, a lot of people have this preconceived notion about wizards that they are somehow weak and feeble and necessarily physically frail, but that's not true in 5e. Somehow the "I can't use a spear!" weapon proficiency gets in people's heads as an insurmountable obstacle to making a given spell-using character type the Wizard class. It's really a very minor thing to change.